Question 118310
{{{(d+2)(d-5)=-6}}} Start with the given equation



{{{d^2-3d-10=-6}}} Foil



{{{d^2-3d-10+6=0}}} Add 6 to both sides



{{{d^2-3d-4=0}}} Combine like terms


{{{(d-4)(d+1)=0}}} Factor the left side (note: if you need help with factoring, check out this <a href=http://www.algebra.com/algebra/homework/playground/change-this-name4450.solver>solver</a>)




Now set each factor equal to zero:

{{{d-4=0}}} or  {{{d+1=0}}} 


{{{d=4}}} or  {{{d=-1}}}    Now solve for d in each case



So our answer is 

 {{{d=4}}} or  {{{d=-1}}} 





Check:

Let's check the first solution {{{d=4}}}

{{{(d+2)(d-5)=-6}}} Start with the given equation



{{{(4+2)(4-5)=-6}}} Plug in the first solution {{{d=4}}}



{{{(6)(-1)=-6}}} Combine like terms



{{{-6=-6}}} Multiply. Since the two sides of the equation are equal, this verifies our answer.



-----------



Now let's check the second solution {{{d=-1}}}

{{{(d+2)(d-5)=-6}}} Start with the given equation



{{{(-1+2)(-1-5)=-6}}} Plug in the second solution {{{d=-1}}}



{{{(1)(-6)=-6}}} Combine like terms



{{{-6=-6}}} Multiply. Since the two sides of the equation are equal, this verifies our answer.



So both of our answers have been verified.